Multi-level characteristic basis function method (MLCBFM) for the anaylsis of large antenna arrays

A multi-level version of the Characteristic Basis Function Method (CBFM) is presented for computing the input impedance matrix and radiation patterns of very large antenna arrays. Specifically, we consider the challenging problem of an electrically large subarray that is surrounded by (many) other disjoint subarrays, and solve this problem by employing a two-level Characteristic Basis Function Method. At level zero, Rao-Wilton-Glisson (RWG) basis functions are employed to locally synthesis the surface current. Next, the number of degrees of freedom (DoFs) for the current is reduced at level one by employing the characteristic basis functions (CBFs), each of which is a macro basis function supported by an antenna element, and is a fixed combination of RWG basis functions. Moreover, the characteristic basis functions at level two are supported by subarrays to further reduce the degrees of freedom. This multilevel approach is memory efficient and generates a final reduced matrix equation that can be solved directly, i.e., in-core through standard Gaussian elimination techniques, even though the conventional MoM (Method of Moments) formulation of the same problem may require more than one million RWG basis functions. Numerical examples are presented for various array sizes, including a 25 subarray problem comprised of 64 tapered-slot antennas (TSAs) each. The proposed method demonstrates very good accuracy, numerical efficiency, and a reduced memory storage requirement.